More gumf from the Grauniad. Supposedly based on something in PNAS: anyone seen it? The usual suspects: the Potsdam folk and Tim Lenton and so on. Sadly (?) the online version doesn’t have the appalling map that the print edition has, featuring highly implausible timescales for those bits I know anything about (Greenland and W Ant gone in 300 years). One of the dangerous tipping points was the greening of the Sahara, errrrm, because that could lead to dangerously low food prices? Shurely shom mishtake. I’m being unfair: that gets a mention (in print) as a rare beneficial example.

Anyway, I await the PNAS version to see if there really is anything new.

Update: for those who haven’t lost the will to live, the proof is at http://researchpages.net/media/resources/2008/02/05/final_proof.pdf

And the search for a meaningful definition of tipping point continues.
As before, the first step is to rename tipping points into tipping elements. Then we try to define it:

A system S is a tipping element if the following condition is met: The parameters controlling the system can be transparently combined into a single control P, and there exists a critical control value Pcrit from which any significant variation by dP > 0 leads to a qualitative change (Fˆ ) in a crucial system feature F, after some observation time T > 0, measured with respect to a reference feature at the critical value, i.e.,

[1] | F(P > Pcrit + dP|T) – F(Pcrit|T) | >= F^ > 0

This inequality applies to forcing trajectories for which a slight deviation above a critical value that continues for some time inevitably induces a qualitative change. This change may occur immediately after the cause or much later.

Hmm, makes you long for the clarity of Aristotle, no? What to make of it?

First to note, that later on 3 extra conditions and tacked on to make “policy relevant tipping points”, but they are a bit dull so I’ll ignore them.

F^ is a “qualitative change” but clearly also a quantitative one, since it needs to have a numerical value. So already we are in arbitrary land: anyone can define anything as qualitative, since it appears to mean “something we care about”. But also, I can’t see any discussion of what values F^ might take (can you?). I looked at the sea ice and Greenalnd sections, and don’t see what values might be being proposed. If you don’t know F^, the definition becomes meaningless.

The formala bears a resemblance to limits stuff from analysis, but sadly you can’t use it like that, of course, because of natural variability. So dP cannot be infinitesimal, and L et al decide that we can all agree that dP ~ 0.2 oC is reasonable (in the cases they consider P is a temperature-like variable). So what it reduces to, in the absence of any idea of what they mean by F^, is that if you perturb the temperature by an amount bigger than natural variabilty, then the system will change.

Which is the bleedin’ obvious.

Oh, and timescales. There is nothing new. The paper says that Gr or WAnt disintegration will take >300 years. Predicatably, the Grauniad removed the “>” sign. And the 300 years lower estimate? Its from Hansen. At least they didn’t take his with-a-century stuff seriously.

haven’t read the article yet, but at first look i’m at least surpised by the collapse of the west african monsoon while the sahara greens (where’s the rain going to come from?) and in 10 years ! you should tell the AMMA folks….

[At a guess, this is a shift of the rain band, which would account for the wetting and drying next to each other -W]

about the WAM: in the vizy & cook paper lenton refers to, they test the 20 IPCC AOGCM, and select only 3 (!) of them on their ability to correctly simulate 20th century WAM. On these 3, Lenton refers mainly to the 2nd one (sudden drying along the Guinea Coast while increased westerly flow from the atlantic allows for a wetter sahel).
Actually V&C clearly say this is not the most reliable: they “prefer” the third model, with no general trend but twice as frequent dry sahelian summer as today.

Does the Sahara even have anything like soil left anymore? I would have thought a green Sahara would take decades or centuries to build up, which would mean that the “warming will be good for us” people would have a bottleneck to go through, rather than a neevrending wonderful world.

guthrie — Yes, in many parts. The Chinese have tken up planting and sucessfully growing sand willow along the eastern edges of the Gobi desert. The same should work in the Saheel, the southern margins of the Sahara.

Plans are afoot to start planting something, not necessarily sand willow, in the Saheel. The investors obtain carbon credits. Details may be searchd for on

One of my buddies in the urban forestry field did his Peace Corps in the Sahel. I wouldn’t start counting my carbon credit chickens before they hatch, if his enjoyable stories are half-true.

William: tipping points, ecologically, are where ecosystems ‘flip’ from one state to another. The ‘another’ state is usu. considered unstable, and as humans haven’t experienced this state, is inherently undesirable, esp. wrt economic issues (economic planning is moot, as indicators are out the window).

One of several things that gets up my nose is the presumption that if places warm and the reainfall changes etc, that we can just deal with it. In reality, farmers would have to learn to grow new crops (Not the easiest thing in the world) using different machinery, and different crop cycles. Meanwhile, drainage and water supplies would change, and more people would install air conditioning etc.
Has anyone done any studies on the actual cost of such adaptations?

Though it is different that the other “tipping elements” in the list, as it would not have major implications for the rest of the climate system, do you think the degradation of the world’s coral reefs (with 1-2 C warming and 500-550 ppm CO2) count as a tipping element? For one, there’s far more agreement on coral reef sensitivity, than on, say, the Amazon dieback, which is mostly only found in the Hadley simulations (?)

[It seems to me that this would be a useful test of the meaningfulness of their definition. They pretend to have produced an objectiev, useable definition. So… apply it. Whereupon you discover (I think) that you cannot do so unambiguously. So I think that the answer is that “tipping element” still lacks a meaningful defn -W]